Magnetic resonance imaging (MRI) devices apply a main magnetic field through an examination region. This strong field, typically denoted B0, acts to align the nuclei within a subject to be examined. In some MRI devices, the B0 field is horizontally oriented, and in others it is vertically oriented.
In both horizontally and vertically oriented systems, magnetic resonance is excited in the aligned nuclei by a relatively strong orthogonal RF field, typically denoted B1. The B1 field causes the aligned nuclei or spins to tip into an plane orthogonal to the static magnetic field B0. Over time, the spins realign themselves with the B0 field emitting relatively weak radio frequency (RF) resonance signals as they process. This resonance is detected by RF coils tuned to the specific resonance frequency desired. These resonance signals are passed to image processing equipment to reconstruct the signals into an image representation for display on a video monitor.
Generally, a direct digital receiver (DDR) comprising an analog-to-digital converter (ADC) that samples the MR signal directly (i.e., without used of an intermediate frequency) and a subsequent digital down converter (DDC) is used to convert the analog MR signal to a digital base-band signal. The sampling frequency (fS), or frequency at which the ADC is operated, is typically much lower than the carrier frequency (fC). According to the Nyquist-Shannon sampling theorem the sampling frequency need only be twice the signal bandwidth (BW) and consequently may be less than the carrier frequency. For MR, the signal bandwidth (limited by the maximum gradient strength and maximum field-of-view) is typically much less than the carrier frequency (defined by the main field strength).
It is common practice to operate the entire DDR at the sampling frequency. In addition the operating frequency is commonly restricted to multiples of a common frequency used to control the timing of the pulse sequences controlling the MR procedure. The combination of these two practices places severe constraints on the design of the anti-aliasing filter required to condition the RF signal prior to digitization.